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Learn how to solve problems step by step online. Find the derivative of (7^m+(21^m)/(21^m)63^m)^(1/m)^(-4). Simplifying. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative \frac{d}{dm}\left(\left(7^m+1+63^m\right)^{\frac{1}{m}}\right) results in \frac{\left(\left(\ln\left(7\right)7^m+4.1431347\cdot 63^m\right)m+\left(- 7^m-1- 63^m\right)\ln\left(7^m+1+63^m\right)\right)\left(7^m+1+63^m\right)^{\left(\frac{1}{m}-1\right)}}{m^2}. Multiplying the fraction by -4\left(\left(7^m+1+63^m\right)^{\frac{1}{m}}\right)^{-5}.
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